While it seems doubtful that people will last that long, in 10^78 years, one would think those people alive at the time would want the universe to continue.
Agreed. It is so highly unlikely that the probability is effectively zero.
Let's give everyone the benefit of the doubt and assume that humanity can exist a thousand times longer than your estimate, say 3x10^9 years. That's about as long as we think life has existed on earth, which is a VERY LONG TIME. That said, it's still 1 x 10^-69 of that time period. I think you can see where we're going with this.
No offense intended, but I have a serious question:
Why would you hope this? This hope seems to me a vestige of the desire of some humans for immortality. And why would it matter to folks whether some sort of intelligence existed this incomprehensibly far into the future?
I think a bigger question is what will they do for that long?
All the things like stars will be long gone and dead before that time leaving us with long lived black holes and radiation. So everything would be based on virtual world can computation by that point. Do you just cool everything to near absolute zero and run it as slow as possible to you can last as long as possible?
The History of the Universe channel has an episode around this, but I'll have to figure out which one it was.
